ORLANDO, Fla. — They worship at the political altar of Ronald Reagan, but Newt Gingrich and Mitt Romney ignore one part of his creed: his so-called 11th Commandment forbidding criticism of fellow Republicans.

"Thou shalt not speak ill of any fellow Republican," Reagan used to say.

This year's two top GOP presidential candidates propose largely similar agendas: Cut taxes. Slash government spending and regulation. Repeal the new health care law.

Yet they're locked in a blood feud that centers on personal history — charges that Gingrich is unethical and a political opportunist and that Romney is a flip-flopping liberal and a rich robber baron — rather than on differences over policy.

Their constant sniping at one another has some Republican voters worrying that it all will weaken the eventual winner heading into the fall campaign against President Barack Obama.

"Stay on subjects people want to hear," James Siemund said this week at a Florida town hall meeting featuring John McCain acting as a surrogate for Romney. "We don't want to hear the bashing."

"It's now mud wrestling, and that is not good," said McCain, the senator from Arizona and his party's 2008 presidential nominee. "It drives up the unfavorables and prevents all of them from being able to present their positive agenda for America."

Both candidates have suffered in the eyes of voters.

The total of Florida voters with a favorable opinion of Gingrich dropped from 59 percent three weeks ago to 51 percent this week, according to polls by Quinnipiac University. At the same time, the ranks of Florida voters with an unfavorable opinion of him jumped from 29 percent to 42 percent.

For Romney, Florida voters viewing him favorably dropped from 73 percent to 64 percent, and his unfavorable total rose from 14 percent to 25 percent.

One reason for the personal attacks, of course, is that the candidates and their allies believe they work. The deluge of attacks on Gingrich wiped out the lead he held briefly in Florida immediately after his Jan. 21 victory in South Carolina.

Sandy Drewnowski, a Republican voter who showed up to hear McCain, admitted that the broadsides against Gingrich pushed her toward Romney. "I was leaning a little to one candidate (Gingrich), but now I may be going the other way," she said. "Just some of the stuff that was pointed out bothered me."

Rough and tumble politics isn't new, of course.

The 19th century was filled with nasty campaign attacks. "Politics ain't bean bag," Finley Peter Dunne wrote in 1895, a still oft-cited quote.

Reagan ran into it in his first primary for governor of California in 1966, when one GOP opponent suggested that he was unstable, calling him "temperamental and emotionally upset." Gaylord Parkinson, the chairman of the California Republican Party at the time, first suggested the 11th Commandment, and Reagan became a disciple.

Well, sort of.

When he challenged President Gerald Ford for the Republican nomination in 1976, Reagan broke his own commandment after losing a string of primaries. Reagan went on the attack — in Florida, coincidentally. He said he didn't trust Ford's leadership, that he lacked vision.

Reagan did not win that primary, or the nomination, that time. Ford supporters blamed the Reagan-inspired split in the party for costing Ford the general election.

Does that mean the same thing will happen to Republicans this time? Not necessarily.

George W. Bush and McCain fought through some bitter primaries in 2000 — the South Carolina primary in particular featured some very nasty under-the-radar attacks on McCain. Bush won it — and went on to win the general election, albeit in a cliffhanger when he lost the popular vote but won the Electoral College, thanks to a Supreme Court ruling — on Florida.

In 2008, Democrats Hillary Clinton and Barack Obama fought through 57 caucuses and primaries, including a hard fight in South Carolina that featured charges that Bill Clinton was playing a race card against Obama. Yet after that fierce intraparty fight, Democrats united behind Obama, who went on to win the general election handily.

Adam Putnam, the Florida commissioner of agriculture and a Romney supporter, said the current tough campaign ultimately will help the winning nominee by making him a better candidate.

"Primaries are a brutal, difficult, practically inhumane process, but it prepares them to face Obama and the Democrats," he said.

The key question may be how the losing candidate reacts once the battle's over — whether he swallows hard and backs the winner, keeps firing at him or sinks into a sullen silence.

"I don't think the rhetoric has gone so far down the road that it's not repairable," said Brad Coker, a Florida-based pollster. "It is only January. There's plenty of time for wounds to heal. But a lot depends on the candidates who do not win."

(David Lightman and Lesley Clark of the Washington Bureau contributed.)